If ∫ e x ( ln x + x ln x + 1 ) d x = f ( x ) + C and f ( 1 ) = 0 , find f ( e ) .

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MathematicsIndefinite IntegrationManipulating IntegrandsEasy2 minQB

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If $\int e^{x} (ln x + x ln x + 1) d x = f (x) + C$ and $f (1) = 0$ , find $f (e)$ .

Answer:

Solution:

The integrand is $d (e^{x} x ln x) / d x$ . The normalization gives $f (x) = e^{x} x ln x$ , so $f (e) = e^{e + 1}$ .

Stream:JEESubject:MathematicsTopic:Indefinite IntegrationSubtopic:Manipulating Integrands

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